Time-varying individual effects in a panel data probit model with an application to female labor force participation

In this article, we study a panel data probit model with time-varying individual effects. Under a Gaussian assumption on the error term, we show the common slope coefficients and time factors can be identified up to scale. We propose for the identified parameters a multi-stage estimation procedure. The proposed estimators have a closed form expression, thus are very convenient to compute even in large samples. We establish the root-n consistency as well as asymptotically normality for these estimators. Using a German socioeconomic panel dataset, we estimate the labor supply function for married women. We find that the unobserved skill premium is positive and shows an upward trend during 2008?2012, in support of the biased technological progress hypothesis.